Tim Wu in this Slate article describes in detail the differences between YouTube and Napster and why he believes that YouTube has very solid legal footing. Wu simply says the YouTube has a safe harbor provision in the DMCA protecting them, while  He also describes the "Bell lobbyists" and how their efforts set the foundation for YouTube's seemingly successful business model. 

The Bell lobbyists, Wu writes, fought one of the greatest copyright struggles in history when it took on Hollywood over the liability of internet companies for copyright infringement.  Wu describes the clash of these two entities as "Frazier meeting Foreman", saying that the unstoppable force that was the Hollywood lobbying team finally met an immovable object in the Bell lobbyists.  Hollywood, on one side, wanted internet sites to be responsible for all content on their site, even if they were unaware of the infringing content.  The Bell lobbyists insisted that this was ludacris and fought against Hollywood's lobbyists with all their political might.  A stalemate insued, so a compromise was reached.  Wu writes that this compromise would later become Title II of the DMCA, which states that companies are protected by a "notice and takedown" system.  This means that all a site has to do to comply with copyright laws is take down infringing material at the request of the copyright holders.  Therefore, YouTube only needs to quickly takedown any material after notified to avoid legal issues. 

Wu does mention that this provision is not 100% "air-tight" noting that if YouTube knows there is infringing material on its site and fails to act, it may be liable in court for the infringement.  Wu then describes the difference between Napster and YouTube, saying that if the Internet were a red-light district, Napster would be the "pimp" and YouTube the "hotel".  He says that while Napster, like a pimp, is a means of getting illegal things and nothing else, YouTube is like the hotel in that they only "provides the space for people to do things, legal or not".